(1). Field of the Invention
The present invention relates to systems and methods of demodulation and in particular, to a demodulation system and method for demodulating an undersampled, modulated carrier signal to recover a signal of interest.
(2). Description of the Prior Art
In communication systems, modulation is commonly used to transmit information from an information source, such as a sensor system where information is detected, to an information destination, such as a receiver system where detected signals are received and processed. According to conventional modulation techniques, a signal of interest detected by a sensor modulates a carrier signal by modifying one or more characteristics of the carrier signal, such as amplitude, frequency or phase, to form a modulated carrier signal. The modulated carrier signal is then more easily transmitted over the appropriate communication channels to the destination or receiver system where the modulated carrier signal is demodulated to recover the signal of interest and determine the information.
One type of sensor system that employs modulation techniques includes fiber optic sensors, for example, as used in fiber optic interferometers for distance measurements. The fiber optic sensors detect or sense light signals that modulate the output phase of the sensor system or interferometer. The modulated carrier can then be photodetected and transmitted to a receiver system. In a system having an array of sensors, the signals are often multiplexed, for example, using time division multiplexing (TDM) and/or wavelength division multiplexing (WDM).
One type of modulation technique used in interferometers and other sensor systems uses phase generated carriers. The sensor's time varying phase signal (signal of interest) modulates the phase generated carriers to form a modulated carrier. Both the signal of interest and the phase generated carriers can be mathematically represented as a Bessel series of harmonically related terms. During modulation, the Bessel series of the signal of interest modulates the Bessel series of the phase generated carrier. The number of terms in the Bessel series of the resulting modulated carrier will be dependent upon the level of the measured or detected signal of interest. The harmonically related terms in the Bessel series of the modulated carrier represent both the measured or detected signal of interest and the carrier signal.
The homodyne receiver concept is typically used to demodulate the sensor information or signal of interest from an adjacent pair of modulated carriers. According to prior art demodulation techniques, a quadrature pair of modulated carriers must be multiplied by a local oscillator of the proper frequency, phase and amplitude. Matching the phase of the local oscillator with the phase of the modulated carrier is often tedious and inexact. If either the phase or amplitude are mismatched, the harmonic distortion of the demodulator will be increased.
Typical fiber optic sensor systems using phase generated carriers to transmit a detected or measured signal (i.e., signal of interest) to a receiver system have used a pair of quadrature carriers with frequencies of either .omega..sub.c and 2.omega..sub.c or 2.omega..sub.c and 3.omega..sub.c, where .omega..sub.c is the phase generated carrier frequency. In multiplexed sensor systems, the sensor sampling frequency f.sub.s must be selected to ensure that frequencies greater than f.sub.s /2 are not aliased into the band of interest below f.sub.s /2. Previous sampling frequencies were, therefore, greater than or equal to four times the frequency of the lowest frequency quadrature carrier. If carriers having a frequency of .omega..sub.c and 2.omega..sub.c are used, for example, a minimum sampling frequency of 4.omega..sub.c is required. Such a high sampling frequency often places great demands on the sampling circuitry.